Diet is the Most Important Aspect of Your Oral Hygiene.
Since you will have little access to fancy oral hygiene products, it is best to adapt your diet for optimal oral health. This means mostly fish and green vegetables; I would limit my consumption of fruits (especially citrus fruits) to limit the exposure of teeth to acids. Avoid certain types of foods where the seeds, or portions of the husk could embed themselves in you gums by accident and cause an abscess if I couldn’t get it out.
Use What You Can to Clean Your Teeth (unless some luggage washes ashore).
Getting the spaces between teeth clean as best you can is extremely important. If you have ever seen apes on TLC flossing with their body hair, you’ll know that this is a potential option if you can find a hair long enough and coarse enough. You could also use a fish bone (or another thin animal bone) like a toothpick. To clean the other surfaces of your teeth, you can use parts of your clothing to rub your teeth or you can also use something like a chewing stick to clean teeth (depending on what kind of foliage is on the island). Chewing sticks were used to clean teeth prior to toothbrushes and some use them today. They are very harsh on your teeth and gums, so be careful. You could use any stick by fraying the end, but typically trees with antimicrobial properties are used: Gum tree, Tea Tree, Neem, SalvadoraPersica, Dakhaar, Cinnamon, Dogwood, Olive, Walnut, and other trees with bitter roots.
Use Ocean Water as a Mouthwash.
Although a salt water rinse won’t do much for bacteria growing on your teeth, it will help you maintain healthy gums, especially if you are using chewing sticks to clean your teeth. Also using a rinse will help flush out food from in between teeth.